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This Week’s Citation Classic
CC/NUMBER 22
MAY 28, 1979
Collins V P, Loeffler R K & Tivey H. Observations on growth rates of human tumors.
Amer. J. Roentgenol. 76:988-1000, 1956.
[Baylor University College of Medicine, Department of Radiology, Houston, TX]
Linear exponential growth, determined by
measurement of pulmonary metastases and
expressed as ‘Doubling Time,’ is introduced as
a characteristic of the individual cancer,
governing the duration before and after
diagnosis. The evidence for an age-related
‘Period of Risk’ for childhood tumors is a
supporting application. [The SCI® indicates
that this paper has been cited over 165 times
since 1961.]
V.P. Collins
9200 Westheimer
Houston, TX 77063
July 27, 1978
“The origin of the concept of linear
exponential growth as a governing
characteristic of cancer cannot be recalled but
the thesis was developing, and data
accumulating, from 1950 on under the
influence of the varied background of the
authors in pathology [Collins], physics [Tivey],
mathematics and bio-statistics [Loeffler].
Simply stated, the rule to be tested was that
the growth of cancer was linear and
exponential with a constant growth rate, as a
characteristic of the individual cancer as its
morphology, governing the duration of cancer
before and after the time of diagnosis. With
confirmation of clinical applicability, the
literature has given the accolade of ‘law,’
better perhaps than Murphy’s but not as
reliable as Newton’s. The ultimate acceptance
must be ascribed to its simplicity and clinical
applicability. Growth is a synonym for cancer.
Growth is a function of time and increasing
volume and both are measurable. There is a
ready measure of growth rate in ‘doubling
time.’
“The rule explains the phenomenon of the
dormant cancer; the total duration of cancer is
approximately 40 doublings; three quarters of
this time is in the period of silent, steady
growth that occurs before the recognition of
the small (but not early) cancer. It explains the
phenomenon of the cancer ‘that suddenly
began to grow wildly;’ this is the exponential
upsweep after 35 to 40 doublings. It explains
the paradox of earlier diagnosis and everimproving survival rates but unrelenting
mortality rates, such as characterize breast
cancer. To move diagnosis to the left on the
exponential curve is to start the countdown on
survival at an earlier point in time, to increase
survival time even without treatment, and to
mask the effect of treatment with unearned
credit.
“There is particular appeal in the
implications for childhood tumors. The ‘Period
of Risk’ thesis (that recurrence, if going to
occur, should develop within a period equal to
the age at diagnosis plus nine months) evolved
in a search for justification for extrapolation of
linear exponential growth back to the time of
inception; several series seem to corroborate
the rule. It also un-masks the error in assuming
that childhood tumors are uniformly malignant
and rapidly growing for lack of a sturdy host
reaction. In this age group all tumors must
grow rapidly; a child is not old enough for a
slowly growing cancer to have reached the
size of recognition; slowly growing cancers
have not had time to traverse their
characteristic period of silent growth when this
is greater than the age of the child.
“Simplicity was the merit of the thought and
the obstacle to its acceptance. On first
submission for publication, it was returned with
a comment to the effect that ‘I have read this
through twice and would not touch it because
we do not accept this sort of material.’
“In the arena of cancer research the initial
impact was approximately that of a
presentation on fire-making with two sticks,
offered at a convention of nuclear physicists.
The simplicity of the hypothesis does assault
the accepted infinite complexity of etiology,
biochemistry and cyto-kinetics of cancer. But
until nuclear physicists solve our energy
problem, there is some practical application for
the warmth of a small fire kindled with two
sticks.”
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